Fractional diffusion modeling of ion channel gating

An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe non-exponential, power-law like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter and Oswald [Proc. Natl. Acad. Sci. USA 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous time random walk composed of nearest neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. USA 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time-regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

LRIG1 is a gatekeeper to exit from quiescence in adult neural stem cells

Adult neural stem cells (NSCs) must tightly regulate quiescence and proliferation. Single-cell analysis has suggested a continuum of cell states as NSCs exit quiescence. Here we capture and characterize in vitro primed quiescent NSCs and identify LRIG1 as an important regulator. We show that BMP-4 signaling induces a dormant non-cycling quiescent state (d-qNSCs), whereas combined BMP-4/FGF-2 signaling induces a distinct primed quiescent state poised for cell cycle re-entry. Primed quiescent NSCs (p-qNSCs) are defined by high levels of LRIG1 and CD9, as well as an interferon response signature, and can efficiently engraft into the adult subventricular zone (SVZ) niche. Genetic disruption of Lrig1 in vivo within the SVZ NSCs leads an enhanced proliferation. Mechanistically, LRIG1 primes quiescent NSCs for cell cycle re-entry and EGFR responsiveness by enabling EGFR protein levels to increase but limiting signaling activation. LRIG1 is therefore an important functional regulator of NSC exit from quiescence

Growth hormone responsive neural precursor cells reside within the adult mammalian brain

The detection of growth hormone (GH) and its receptor in germinal regions of the mammalian brain prompted our investigation of GH and its role in the regulation of endogenous neural precursor cell activity. Here we report that the addition of exogenous GH significantly increased the expansion rate in long-term neurosphere cultures derived from wild-type mice, while neurospheres derived from GH null mice exhibited a reduced expansion rate. We also detected a doubling in the frequency of large (i.e. stem cell-derived) colonies for up to 120 days following a 7-day intracerebroventricular infusion of GH suggesting the activation of endogenous stem cells. Moreover, gamma irradiation induced the ablation of normally quiescent stem cells in GH-infused mice, resulting in a decline in olfactory bulb neurogenesis. These results suggest that GH activates populations of resident stem and progenitor cells, and therefore may represent a novel therapeutic target for age-related neurodegeneration and associated cognitive decline

Transgene Excision Has No Impact on In Vivo Integration of Human iPS Derived Neural Precursors

The derivation of induced human pluripotent stem cells (hiPS) has generated significant enthusiasm particularly for the prospects of cell-based therapy. But there are concerns about the suitability of iPS cells for in vivo applications due in part to the introduction of potentially oncogenic transcription factors via viral vectors. Recently developed lentiviral vectors allow the excision of viral reprogramming factors and the development of transgene-free iPS lines. However it is unclear if reprogramming strategy has an impact on the differentiation potential and the in vivo behavior of hiPS progeny. Here we subject viral factor-free, c-myc-free and conventionally reprogrammed four-factor human iPS lines to a further challenge, by analyzing their differentiation potential along the 3 neural lineages and over extended periods of time in vitro, as well as by interrogating their ability to respond to local environmental cues by grafting into the striatum. We demonstrate similar and efficient differentiation into neurons, astrocytes and oligodendrocytes among all hiPS and human ES line controls. Upon intracranial grafting in the normal rat (Sprague Dawley), precursors derived from all hiPS lines exhibited good survival and response to environmental cues by integrating into the subventricular zone, acquiring phenotypes typical of type A, B or C cells and migrating along the rostral migratory stream into the olfactory bulb. There was no teratoma or other tumor formation 12 weeks after grafting in any of the 26 animals used in the study. Thus neither factor excision nor persistence of c-myc impact the behavior of hiPS lines in vivo.United States. National Institutes of HealthNew York State Stem Cell ScienceNational Institute of Neurological Disorders and Stroke (U.S.)Starr Foundation (Tri-Institutional Starr Stem Cell Scholars Fellowship

Enhancement of endogenous neurogenesis in ephrin-B3 deficient mice after transient focal cerebral ischemia

Cerebral ischemia stimulates endogenous neurogenesis. However, the functional relevance of this phenomenon remains unclear because of poor survival and low neuronal differentiation rates of newborn cells. Therefore, further studies on mechanisms regulating neurogenesis under ischemic conditions are required, among which ephrin-ligands and ephrin-receptors (Eph) are an interesting target. Although Eph/ephrin proteins like ephrin-B3 are known to negatively regulate neurogenesis under physiological conditions, their role in cerebral ischemia is largely unknown. We therefore studied neurogenesis, brain injury and functional outcome in ephrin-B3−/− (knockout) and ephrin-B3+/+ (wild-type) mice submitted to cerebral ischemia. Induction of stroke resulted in enhanced cell proliferation and neuronal differentiation around the lesion site of ephrin-B3−/− compared to ephrin-B3+/+ mice. However, prominent post-ischemic neurogenesis in ephrin-B3−/− mice was accompanied by significantly increased ischemic injury and motor coordination deficits that persisted up to 4 weeks. Ischemic injury in ephrin-B3−/− mice was associated with a caspase-3-dependent activation of the signal transducer and activator of transcription 1 (STAT1). Whereas inhibition of caspase-3 had no effect on brain injury in ephrin-B3+/+ animals, infarct size in ephrin-B3−/− mice was strongly reduced, suggesting that aggravated brain injury in these animals might involve a caspase-3-dependent activation of STAT1. In conclusion, post-ischemic neurogenesis in ephrin-B3−/− mice is strongly enhanced, but fails to contribute to functional recovery because of caspase-3-mediated aggravation of ischemic injury in these animals. Our results suggest that ephrin-B3 might be an interesting target for overcoming some of the limitations of further cell-based therapies in stroke

Long-Term Impact of Radiation on the Stem Cell and Oligodendrocyte Precursors in the Brain

Background. The cellular basis of long term radiation damage in the brain is not fully understood. Methods and Findings. We administered a dose of 25Gy to adult rat brains while shielding the olfactory bulbs. Quantitative analyses were serially performed on different brain regions over 15 months. Our data reveal an immediate and permanent suppression of SVZ proliferation and neurogenesis. The olfactory bulb demonstrates a transient but remarkable SVZ-independent ability for compensation and maintenance of the calretinin interneuron population. The oligodendrocyte compartment exhibits a complex pattern of limited proliferation of NG2 progenitors but steady loss of the oligodendroglial antigen O4. As of nine months post radiation, diffuse demyelination starts in all irradiated brains. Counts of capillary segments and length demonstrate significant loss one day post radiation but swift and persistent recovery of the vasculature up to 15 months post XRT. MRI imaging confirms loss of volume of the corpus callosum and early signs of demyelination at 12 months. Ultrastructural analysis demonstrates progressive degradation of myelin sheaths with axonal preservation. Areas of focal necrosis appear beyond 15 months and are preceded by widespread demyelination. Human white matter specimens obtained post-radiation confirm early loss of oligodendrocyte progenitors and delayed onset of myelin sheath fragmentation with preserved capillaries. Conclusions. This study demonstrates that long term radiation injury is associated with irreversible damage to the neural stem cell compartment in the rodent SVZ and loss of oligodendrocyte precursor cells in both rodent and human brain. Delayed onset demyelination precedes focal necrosis and is likely due to the loss of oligodendrocyte precursor

Directing Astroglia from the Cerebral Cortex into Subtype Specific Functional Neurons

Forced expression of single defined transcription factors can selectively and stably convert cultured astroglia into synapse-forming excitatory and inhibitory neurons

Mechanisms Used for Genomic Proliferation by Thermophilic Group II Introns

Studies of mobile group II introns from a thermophilic cyanobacterium reveal how these introns proliferate within genomes and might explain the origin of introns and retroelements in higher organisms